# Probability of observing the same value for 10th percentile in two different samples

Edited:

I have a categorical variable comprising of values from 1 to 7 with these probability:

score   1        2       3      4       5       6   7
p       0.01    0.01    0.03    0.05    0.2   0.3   0.4


In two different samples from the two different populations, I found the same value for 10th percentile (i.e. 4) in observed data. I want to find the likelihood of having exactly the same value for 10th percentile.

FYI, the scores are answers to a scale and probabilities are proportions for each category in a normative sample.I want to be able to do this in R.

P.S.: any suggestion on calculating cumulative distribution of a variable with above-mentioned properties is appreciated.

Thanks.

• Do you mean 'at least 10%', 'at most 10%' or 'exactly 10%'? Dec 14, 2013 at 6:29
• @Glen_b I meant exactly 10% but would be happy to learn other possibilities like 'at least 10%' and 'at most 10%'.
– Amin
Dec 14, 2013 at 6:45
• The proportion of times that exactly 1000 observations out of 10000 fall below 4 will be quite small (it's actually possible to compute this number, there's no need to simulate it). Dec 14, 2013 at 6:47
• @Glen_b The reason is that in a survey from two different samples from two different populations I found the same value for 10th percentile. I want to know how likely is to find the same value for 10th percentile in a variable.This is why I thought that a simulation would be proper.
– Amin
Dec 14, 2013 at 6:49
• Finding the same value for the 10th percentile is rather different from what you're asking about. Dec 14, 2013 at 6:50